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200 10$aArbitrary Reference in Logic and Mathematics /$fby Massimiliano Carrara, Enrico Martino
205   $a1st ed. 2024.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024.
215   $a1 online resource (102 pages)
225 1 $aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,$x2542-8292 ;$v490
311 08$aPrint version: Carrara, Massimiliano Arbitrary Reference in Logic and Mathematics Cham : Springer International Publishing AG,c2024 9783031664519 
320   $aIncludes bibliographical references and index.
327   $aPreface -- 1. On Arbitrary Reference -- 2. On Plural Arbitrary Reference -- 3. On Arbitrary Fictional Models -- 4. Second-Order Logic and Plural Arbitrary Reference -- 5. Logical Concepts and Plural Arbitrary Reference -- 6. Plural Arbitrary Reference and mereology -- 7. Grounding Megethology on Plural Arbitrary Reference -- 8. The Mereological foundation of Megethology -- 9. Final ruminations -- Index.
330   $aThis book develops a new approach to plural arbitrary reference and examines mereology, including considering four theses on the alleged innocence of mereology. The authors have advanced the notion of plural arbitrary reference in terms of idealized plural acts of choice, performed by a suitable team of agents. In the first part of the book, readers will discover a revision of Boolos? interpretation of second order logic in terms of plural quantification and a sketched structuralist reconstruction of second-order arithmetic based on the axiom of infinite, a la Dedekind, as the unique non-logical axiom. The work goes on to analyse the pros and cons of the new interpretation, also with respect to Linnebo?s objections to the thesis that second order logic is genuine logic. A theory of concepts that can be labelled as a theory of logical concepts is expounded. In the second part of the book, the authors consider grounding megethology on plural arbitrary reference and argue that the arguments for the ontological innocence of mereology are not conclusive and that ? for a certain use of mereology ? a thesis of innocence, similar to that of plural arbitrary reference, is defensible. The work proposes a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. This considered work will appeal to scholars from branches of analytic philosophy, logic and the philosophy of mathematics in particular.
410  0$aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,$x2542-8292 ;$v490
606   $aAnalysis (Philosophy)
606   $aMathematical logic
606   $aLinguistics
606   $aMathematics$xPhilosophy
606   $aLogic
606   $aAnalytic Philosophy
606   $aMathematical Logic and Foundations
606   $aLinguistics
606   $aPhilosophy of Mathematics
606   $aLogic
615  0$aAnalysis (Philosophy).
615  0$aMathematical logic.
615  0$aLinguistics.
615  0$aMathematics$xPhilosophy.
615  0$aLogic.
615 14$aAnalytic Philosophy.
615 24$aMathematical Logic and Foundations.
615 24$aLinguistics.
615 24$aPhilosophy of Mathematics.
615 24$aLogic.
676   $a160
700   $aCarrara$b Massimiliano$01637230
702   $aMartino$b Enrico
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9910881096503321
996   $aArbitrary Reference in Logic and Mathematics$94256236
997   $aUNINA